Question

assignment #2: triangle proportionality theorem
verify that the given segments are parallel.

1. $overline{ab}$ and $overline{cd}$

(figure: triangle $eab$ with point $c$ on $ea$ (length $ec = 12$, $ca = 4$) and point $d$ on $eb$ (length $ed = 14$, $db = 4\frac{2}{3}$))
$\frac{12}{4} = \frac{14}{4\frac{2}{3}}$ are
options: not equal, therefore the lines are parallel; not equal, therefore the lines are not parallel; equal, therefore the lines are parallel; equal, therefore the lines are not parallel

1. $overline{mn}$ and $overline{qr}$

(figure: triangle $por$ with point $m$ on $po$ (length $pm = 9$, $mo = 2.7$) and point $n$ on $pr$ (length $pn = 10$, $nr = 3$))
$\frac{9}{2.7} = \frac{10}{3}$ are

Explanation:

For Problem 7:

Step1: Simplify left ratio

$\frac{12}{4} = 3$

Step2: Simplify right ratio

$\frac{14}{4\frac{2}{3}} = \frac{14}{\frac{14}{3}} = 14 \times \frac{3}{14} = 3$

Step3: Compare ratios

Since $3=3$, the ratios are equal. By the Triangle Proportionality Theorem converse, $\overline{AB} \parallel \overline{CD}$.

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For Problem 8:

Step1: Simplify left ratio

$\frac{2.7}{9} = 0.3$

Step2: Simplify right ratio

$\frac{3}{10} = 0.3$

Step3: Compare ratios

Since $0.3=0.3$, the ratios are equal. By the Triangle Proportionality Theorem converse, $\overline{MN} \parallel \overline{QR}$.

Answer:

equal, therefore the lines are parallel